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Math 1332

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Math 1332

Draw without lifting your pencil or crossing (or re-tracing) any lines.

Chapter 10.7

Non-Euclidean Geometry

Vertex: the intersection of two or more segments

(edges)

Graph – a combination of vertices and edges

Even Vertex – has an even number of edges

Odd Vertex – has an odd number of edges.

Traversable Graph – can be traced without lifting your pencil and without re-tracing edges

- Rules for Traversability :
- If all vertices are even a graph is traversable
- If you have 2 odd vertices (the rest even) a graph is traversable. Start at one of the odd vertices and end at the other.
- More than two odd vertices is not traversable.

Not Traversable (4 odd)

Traversable (all even)

Topology – looks at shapes as being able to be twisted.

Rules for Topology :

Classify by the number of holes – genus

Genus = 1

Genus = 1

Genus = 4

- Moebus Strip

http://www.metacafe.com/watch/868152/mobius_strip/

http://www.math.psu.edu/dlittle/java/geometry/spherical/toolbox.html

The sum of the angles of a triangle can be more than 180º

http://www.flatlandthemovie.com/